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In this paper, we classified the finite p-groups with exactly one A-subgroup of given structure of order p. [ABSTRACT FROM AUTHOR]

Let U be a quantized enveloping algebra and $$\dot U$$ its modified form. Lusztig gives some symmetries on U and $$\dot U$$ . In view of the realization of U by the reduced Drinfeld double of the Ringel-Hall algebra, one can apply the BGP-reflection functors to the double Ringel-Hall algebra to obtain Lusztig’s symmetries on U and their important properties, for instance, the braid relations. In this paper, we define a modified form [InlineMediaObject not available: see fulltext.] of the Ringel-Hall algebra and realize the Lusztig’s symmetries on $$\dot U$$ by applying the BGP-reflection functors to [InlineMediaObject not available: see fulltext.]. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a type of approximation operators of neural networks with sigmodal functions on compact intervals, and obtain the pointwise and uniform estimates of the approximation. To improve the approximation rate, we further introduce a type of combinations of neural networks. Moreover, we show that the derivatives of functions can also be simultaneously approximated by the derivatives of the combinations. We also apply our method to construct approximation operators of neural networks with sigmodal functions on infinite intervals. [ABSTRACT FROM AUTHOR]

The determinant theory for matrices over a pseudo-complemented distributive lattice is presented. Previous results on this topic are special cases of the theorems proved in this paper. [ABSTRACT FROM AUTHOR]

The Kopytov order for any algebras over a field is considered. The purpose of this paper is to investigate a generalization of the concept of prime radical to lattice ordered algebras over partially ordered fields. Prime radicals of l-algebras over partially ordered and directed fields are described. Some results concerning properties of the lower weakly solvable l-radical of l-algebras are obtained. Necessary and sufficient conditions for the l-prime radical of an l-algebra to be equal to the lower weakly solvable l-radical of an l-algebra are presented. [ABSTRACT FROM AUTHOR]

Consider reduced Abelian p-groups ( p ≥ 3) A and A. In this paper, we prove that the automorphism groups Aut A and Aut A are elementary equivalent if and only if the groups A and A are equivalent in second-order logic bounded by the cardinalities of the basic subgroups of A and A. [ABSTRACT FROM AUTHOR]

An edge-colored graph G is rainbow connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection number of a connected graph G, denoted by rc( G), is the smallest number of colors that are needed in order to make G rainbow connected. In this paper, we proved that rc( G) ≤ 3( n + 1)/5 for all 3-connected graphs. [ABSTRACT FROM AUTHOR]

Motivated both by the work of Anstee, Griggs, and Sali on forbidden submatrices and also by the extremal sat-function for graphs, we introduce sat-type problems for matrices. Let $${\mathcal{F}}$$ be a family of k-row matrices. A matrix M is called $${\mathcal{F}}$$- admissible if M contains no submatrix $${F \in \mathcal{F}}$$ (as a row and column permutation of F). A matrix M without repeated columns is $${\mathcal{F}}$$- saturated if M is $${\mathcal{F}}$$-admissible but the addition of any column not present in M violates this property. In this paper we consider the function sat( $${n, \mathcal{F}}$$) which is the minimal number of columns of an $${\mathcal{F}}$$-saturated matrix with n rows. We establish the estimate sat $${(n, \mathcal{F})=O(n^{k-1})}$$ for any family $${\mathcal{F}}$$ of k-row matrices and also compute the sat-function for a few small forbidden matrices. [ABSTRACT FROM AUTHOR]

The core G of a graph G is the subgraph of G induced by the vertices of maximum degree Δ( G). In this paper, we show that if G is a connected graph with Δ( G) ≤ 2 and $${\Delta(G)\ge\frac12(|V(G)|-1)}$$, then G is of class 2 if and only if G is overfull. Our result generalizes several results of Hilton and Zhao. [ABSTRACT FROM AUTHOR]

Augmented candelabra quadruple systems play an important role in the construction of Steiner 3-designs. In this paper, we consider augmented resolvable candelabra quadruple systems with three even groups and show that the necessary conditions on the existence of ARCQS( g : s) when g is even are also sufficient. [ABSTRACT FROM AUTHOR]

If every vertex cut of a graph G contains a locally 2-connected vertex, then G is quasilocally 2-connected. In this paper, we prove that every connected quasilocally 2-connected claw-free graph is Hamilton-connected. [ABSTRACT FROM AUTHOR]

We consider proper edge colorings of a graph G using colors of the set {1, . . . , k}. Such a coloring is called neighbor sum distinguishing if for any pair of adjacent vertices x and y the sum of colors taken on the edges incident to x is different from the sum of colors taken on the edges incident to y. The smallest value of k in such a coloring of G is denoted by ndi( G). In the paper we conjecture that for any connected graph G ≠ C of order n ≥ 3 we have ndi( G) ≤ Δ( G) + 2. We prove this conjecture for several classes of graphs. We also show that ndi( G) ≤ 7Δ( G)/2 for any graph G with Δ( G) ≥ 2 and ndi( G) ≤ 8 if G is cubic. [ABSTRACT FROM AUTHOR]

The classic lower bounds δ + 1 (Dirac), 2 δ (Dirac) and 3 δ − 3 (Voss and Zuluaga) for the circumference (the order of a longest cycle C in a graph G) are based on the minimum degree δ and some G\ C structures, combined with some additional connectivity conditions. A natural problem arises to find an analogous bound in a general form ( i + 1)( δ − i + 1) with i = 0, 1, . . . , δ, including the bounds δ + 1, 2 δ and 3 δ − 3 as special cases. In this paper we present two tight lower bounds for the circumference just of the form ( i + 1)( δ − i + 1) for each $${i\in\{0,\ldots,\delta\}}$$ based entirely on appropriate G\ C structures, actually escaping any other additional conditions: in each graph G, (i) $${|C|\geq(\overline{p}+1)(\delta-\overline{p}+1)}$$ and (ii) $${|C|\geq(\overline{c}+1)(\delta-\overline{c}+1),}$$ where $${\overline{p}}$$ and $${\overline{c}}$$ denote the orders of a longest path and a longest cycle in G\ C, respectively. [ABSTRACT FROM AUTHOR]

The independence number of a graph G, denoted by α( G), is the cardinality of a maximum independent set, and μ( G) is the size of a maximum matching in G. If α( G) + μ( G) equals its order, then G is a König-Egerváry graph. The square of a graph G is the graph G with the same vertex set as in G, and an edge of G is joining two distinct vertices, whenever the distance between them in G is at most two. G is a square-stable graph if it enjoys the property α( G) = α( G). In this paper we show that G is a König-Egerváry graph if and only if G is a square-stable König-Egerváry graph. [ABSTRACT FROM AUTHOR]

In 1966 T. Gallai asked whether connected graphs with empty intersection of their longest paths do or do not exist. After examples of such graphs were found, the question was extended to graphs of higher connectivity, and to cycles instead of paths. Examples being again found, for connectivity up to 3, the question has been asked whether there exist large families of graphs without Gallai's property. The family of grid graphs, a special kind of graphs embedded in the planar square lattice $${\mathcal {L}}$$ , has been shown by B. Menke to contain no graph enjoying Gallai's property. In this paper we find several examples of graphs embedded in $${\mathcal {L}}$$ and enjoying that property with respect to both paths and cycles. [ABSTRACT FROM AUTHOR]

Let P be a set of n points on the plane in general position, n ≥ 3. The edge rotation graph $${\mathcal{E} \mathcal{R} \mathcal{G}(P,k)}$$ of P is the graph whose vertices are the plane geometric graphs on P with exactly k edges, two of which are adjacent if one can be obtained from the other by an edge rotation. In this paper we study some structural properties of $${\mathcal{E} \mathcal{R} \mathcal{G}(P,k)}$$ , such as its connectivity and diameter. We show that if the vertices of $${\mathcal{E} \mathcal{R} \mathcal{G}(P,k)}$$ are not triangulations of P, then it is connected and has diameter O( n). We also show that the chromatic number of $${\mathcal{E} \mathcal{R} \mathcal{G}(P,k)}$$ is O( n), and show how to compute an implicit coloring of its vertices. We also study edge rotations in edge-labelled geometric graphs. [ABSTRACT FROM AUTHOR]

In 1987, Alavi, Boals, Chartrand, Erdös, and Oellermann conjectured that all graphs have an ascending subgraph decomposition (ASD). Though different classes of graphs have been shown to have an ASD, the conjecture remains open. In this paper we investigate the similar problem for digraphs. In particular, we will show that any orientation of a compete balanced tripartite graph has an ASD. [ABSTRACT FROM AUTHOR]

In this paper we introduce confluence operators, that are inspired by the existing links between belief revision, update and merging operators. Roughly, update operators can be considered as pointwise revision, whereas revision operators can be considered as special case of merging operators. Confluence operators are to merging operators what update operators are to revision operators. Similarly, update operators can be considered as special case of confluence operators just as revision can be considered as special case of merging operators. Confluence operators gives all possible agreement situations from a set of belief bases. [ABSTRACT FROM AUTHOR]

In the current paper, we have investigated the generalized FitzHugh-Nagumo model. We have shown that symmetric bursting behaviors of different types could be observed in this model with an appropriate recovery term. A modified version of this system is used to construct bursting activities. Furthermore, we have shown some numerical examples of delayed Hopf bifurcation and canard phenomenon in the symmetric bursting of super-Hopf/homoclinic type near its super-Hopf and homoclinic bifurcations, respectively. [ABSTRACT FROM AUTHOR]

This paper analyzes the action δ of a Lie algebra X by derivations on a C*-algebra $${\mathcal{A}}$$ . This action satisfies an 'almost inner' property which ensures affiliation of the generators of the derivations δ with $${\mathcal{A}}$$ , and is expressed in terms of corresponding pseudo-resolvents. In particular, for an abelian Lie algebra X acting on a primitive C*-algebra $${\mathcal{A}}$$ , it is shown that there is a central extension of X which determines algebraic relations of the underlying pseudo-resolvents. If the Lie action δ is ergodic, i. e. the only elements of $${\mathcal{A}}$$ on which all the derivations in δ vanish are multiples of the identity, then this extension is given by a (non-degenerate) symplectic form σ on X. Moreover, the algebra generated by the pseudo-resolvents coincides with the resolvent algebra based on the symplectic space ( X, σ). Thus the resolvent algebra of the canonical commutation relations, which was recently introduced in physically motivated analyses of quantum systems, appears also naturally in the representation theory of Lie algebras of derivations acting on C*-algebras. [ABSTRACT FROM AUTHOR]

This paper is devoted to studying the thermodynamic formalism for suspension flows defined over countable alphabets. We are mostly interested in the regularity properties of the pressure function. We establish conditions for the pressure function to be real analytic or to exhibit a phase transition. We also construct an example of a potential for which the pressure has countably many phase transitions. [ABSTRACT FROM AUTHOR]

Many construction methods for (nearly) uniform designs have been proposed under the centered $$L_2$$-discrepancy, and most of them are only suitable for constructing designs with small size. This paper proposes a new method, called mixture method (MM), to construct nearly symmetrical/asymmetrical uniform designs with large number of runs and/or large number of factors. The new method has the 'better than given' property, i.e., the resulting design is better than existing designs in the sense of the pre-decided criterion. Moreover, the computational speed of MM is faster than most existing methods. [ABSTRACT FROM AUTHOR]

In a recent paper, G. Czédli and E. T. Schmidt present a structure theorem for planar semimodular lattices. In this note, we present an alternative proof. [ABSTRACT FROM AUTHOR]

The paper focus on first and second laws analysis for flow and heat transfer inside a vertical channel made of two uniformly porous parallel plates with suction/injection under the combined action of buoyancy force, transverse magnetic field and constant pressure gradient. Both vertical walls are kept isothermal at the same temperatures and the flow of the conducting fluid is assumed to be unsteady with variable viscosity. The nonlinear governing equations in Cartesian coordinate are obtained and solved numerically using semi-implicit finite difference techniques to develop expressions for velocity and temperature profiles. The entropy generation number, irreversibility distribution ratio and Bejan number are presented graphically and discussed quantitatively for various values of the embedded parameters. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notions of sum and direct sum of soft submodules, small soft submodules and radical of a soft module. Moreover, we obtain basic properties of such soft submodules. [ABSTRACT FROM AUTHOR]

This paper presents two algebraic criteria for the input-to-state stability of recurrent neural networks with time-varying delays. The criteria which also ensure global exponential stability when the input u( t) is equal to 0 and is easy to be verified only with the connection weights of the recurrent neural networks. Two numerical examples are given to demonstrate the effectiveness of the proposed criteria. [ABSTRACT FROM AUTHOR]

In this paper, the numerical simulation method is used to study spectral properties of sample covariance matrices. [ABSTRACT FROM AUTHOR]

In this paper, we give discreteness criteria of subgroups of the special linear group on ℚ or ℂ in two and higher dimensions. Jørgensen's inequality gives a necessary condition for a non-elementary group of Möbius transformations to be discrete. We give a version of Jørgensen's inequality for SL( m,ℂ). [ABSTRACT FROM AUTHOR]

This paper presents a number of numerical quantities that admit interpretation in terms of classical and quantum mathematical physics. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a reinsurance strategy into the Sparre Andersen risk model with a horizon dividend barrier, which is named dividend-reinsurance strategy. It is shown that the value function of the new strategy far exceeds that of the optimal barrier strategy (even that of the optimal dividend strategy). Some results on the advantages of the new strategy are obtained, and the methods for computing the value functions are provided. Numerical illustrations for Erlang (2) and compound Poisson risk models are also given. [ABSTRACT FROM AUTHOR]

The paper is concerned with the analysis of a new variational model to restore point-like and curve-like singularities in biological images. To this aim we investigate the variational properties of a suitable energy which governs these pathologies. Finally in order to realize numerical experiments we minimize, in the discrete setting, a regularized version of this functional by fast descent gradient scheme. [ABSTRACT FROM AUTHOR]

It is well known that every inverse semigroup admits an E-unitary cover. In this paper we investigate the analogue of E-unitary covers within the variety of ∨-semilatticed inverse semigroups. [ABSTRACT FROM AUTHOR]

In this paper, we give a characterization of digraphs Q, | Q|≤4 such that the associated Hecke-Kiselman monoids H are finite. In general, a necessary condition for H to be a finite monoid is that Q is acyclic and its Coxeter components are Dynkin diagrams. We show, by constructing examples, that such conditions are not sufficient. [ABSTRACT FROM AUTHOR]

In this paper we introduce the concept of modular translation. With this tool, if we consider a certain numerical semigroup S, we build another one S′ whose principal invariants are given explicitly in terms of the invariants of S. Some results about irreducible numerical semigroups are also studied. [ABSTRACT FROM AUTHOR]

A semigroup S is called η-simple if S has no semilattice congruences except S× S. Tamura in (Semigroup Forum 24:77-82, ) studied η-simple semigroups with a unique idempotent. In the present paper we consider a more general situation, that is, we investigate η-simple semigroups (without zero) with a least idempotent. Moreover, we study η-simple semigroups with zero which contain a least non-zero idempotent. [ABSTRACT FROM AUTHOR]

In this paper, we study finite dimensional approximations of Kohn-Sham models, which are widely used in electronic structure calculations. We prove the convergence of the finite dimensional approximations and derive the a priori error estimates for ground state energies and solutions. We also provide numerical simulations for several molecular systems that support our theory. [ABSTRACT FROM AUTHOR]

R-duals of certain sequences in Hilbert spaces were introduced by Casazza, Kutyniok and Lammers in 2004 and later generalized to Banach spaces by Xiao and Zhu. In this paper we provide some characterizations of R-dual sequences in Banach spaces. [ABSTRACT FROM AUTHOR]

In this paper, we prove the interior regularity for the solution to the Abreu equation in any dimension assuming the existence of the C estimate. [ABSTRACT FROM AUTHOR]

In this paper, we mainly discuss the normality of two families of functions concerning shared values and proved: Let F and G be two families of functions meromorphic on a domain D ⊂ ℂ, a, a, a, a be four distinct finite complex numbers. If G is normal, and for every f ε F, there exists g ε G such that f( z) and g( z) share the values a, a, a, a, then F is normal on D. [ABSTRACT FROM AUTHOR]

In this paper, we consider the real interpolation with a function parameter between martingale Hardy and BMO spaces. An interpolation theorem for martingale Hardy and BMO spaces is formulated. As an application, real interpolation between martingale Lorentz and BMO spaces is given. [ABSTRACT FROM AUTHOR]

In this paper, we prove that some volume-preserving almost Anosov systems are ergodic if they are essentially accessible. The key idea is that there are stable and unstable manifolds with uniform size on the orbits of the hyperbolic points for these systems. [ABSTRACT FROM AUTHOR]

Let M be a closed smooth manifold M, and let f: M → M be a diffeomorphism. In this paper, we consider a nontrivial transitive set Λ of f. We show that if f has the C-stably average shadowing property on Λ, then Λ admits a dominated splitting. [ABSTRACT FROM AUTHOR]

Brattka, Miller and Nies () showed that some major algorithmic randomness notions are characterized via differentiability. The main goal of this paper is to characterize Kurtz randomness by a differentiation theorem on a computable metric space. The proof shows that integral tests play an essential part and shows that how randomness and differentiation are connected. [ABSTRACT FROM AUTHOR]

The aim of this paper is to provide an original method of constructing very effective near-cloaking structures for the conductivity problem. These new structures are such that their first Generalized Polarization Tensors (GPT) vanish. We show that this in particular significantly enhances the cloaking effect. We then present some numerical examples of Generalized Polarization Tensors vanishing structures. [ABSTRACT FROM AUTHOR]

Let G be a (molecule) graph. A perfect matching, or Kekulé structure of G is a set of independent edges covering every vertex exactly once. Enumeration of Kekulé structures of a (molecule) graph is interest in chemistry, physics and mathematics. In this paper, we focus on some polyominos on the torus and obtain the explicit expressions on the number of the Kekulé structures of them. [ABSTRACT FROM AUTHOR]

In this paper we develop and study new high algebraic order multiderivative explicit four-step method with phase-lag and its first, second and third derivatives equal to zero. For the produced methods we investigate their errors and stability. Based on the above mentioned analysis we will arrive to some remarks and conclusions about their the efficiency to the numerical integration of the radial Schrödinger equation. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the bifurcations and dynamic behaviour of travelling wave solutions of the Klein-Gordon-Zakharov equations given in Shang et al, Comput. Math. Appl. 56, 1441 (). Under different parameter conditions, we obtain some exact explicit parametric representations of travelling wave solutions by using the bifurcation method (Feng et al, Appl. Math. Comput. 189, 271 (); Li et al, Appl. Math. Comput. 175, 61 ()). [ABSTRACT FROM AUTHOR]

In this paper, the exact synchronization for a coupled system of wave equations with Dirichlet boundary controls and some related concepts are introduced. By means of the exact null controllability of a reduced coupled system, under certain conditions of compatibility, the exact synchronization, the exact synchronization by groups, and the exact null controllability and synchronization by groups are all realized by suitable boundary controls. [ABSTRACT FROM AUTHOR]

Let TX be the full transformation semigroup on a set X and E be a non-trivial equivalence on X. The set TE (X) = { f ∊ TX : ∀(x,y) ∊ E; ( f (x), f (y)) ∊ E} is a subsemigroup of TX . For a finite totally ordered set X and a convex equivalence E on X, the set of all the orientation-preserving transformations in TE(X) forms a subsemigroup of TE(X) denoted by OPE(X). In this paper, under the hypothesis that the totally ordered set X is of cardinality mn (m,n ≥ 2) and the equivalence E has m classes such that each E-class contains n consecutive points, we calculate the cardinality of the semigroup OPE(X), and that of its idempotents. [ABSTRACT FROM AUTHOR]

Let G = (V1,V2;E) be a bipartite graph with ∣ V1 ∣=∣ V2 ∣= 4k, where k is a positive integer. In this paper, it is proved that if the minimum degree of G is at least 3k+1, then G contains k vertex-disjoint cycles of order eight such that each of them has at least two chords. [ABSTRACT FROM AUTHOR]